Stochastic Modelling of Air Pollution Impacts on Respiratory Infection Risk

The impact of air pollution on people’s health and daily activities in China has recently aroused much attention. By using stochastic differential equations, variation in a 6 year long time series of air quality index (AQI) data, gathered from air quality monitoring sites in Xi’an from 15 November 2010 to 14 November 2016 was studied. Every year the extent of air pollution shifts from being serious to not so serious due to alterations in heat production systems. The distribution of such changes can be predicted by a Bayesian approach and the Gibbs sampler algorithm. The intervals between changes in a sequence indicate when the air pollution becomes increasingly serious. Also, the inflow rate of pollutants during the main pollution periods each year has an increasing trend. This study used a stochastic SEIS model associated with the AQI to explore the impact of air pollution on respiratory infections. Good fits to both the AQI data and the numbers of influenza-like illness cases were obtained by stochastic numerical simulation of the model. Based on the model’s dynamics, the AQI time series and the daily number of respiratory infection cases under various government intervention measures and human protection strategies were forecasted. The AQI data in the last 15 months verified that government interventions on vehicles are effective in controlling air pollution, thus providing numerical support for policy formulation to address the haze crisis.     

Stochastic Modelling of Chromosomal Segregation: Errors Can Introduce Correction

Cell division is a complex process requiring the cell to have many internal checks so that division may proceed and be completed correctly. Failure to divide correctly can have serious consequences, including progression to cancer. During mitosis, chromosomal segregation is one such process that is crucial for successful progression. Accurate segregation of chromosomes during mitosis requires regulation of the interactions between chromosomes and spindle microtubules. If left uncorrected, chromosome attachment errors can cause chromosome segregation defects which have serious effects on cell fates. In early prometaphase, where kinetochores are exposed to multiple microtubules originating from the two poles, there are frequent errors in kinetochore-microtubule attachment. Erroneous attachments are classified into two categories, syntelic and merotelic. In this paper, we consider a stochastic model for a possible function of syntelic and merotelic kinetochores, and we provide theoretical evidence that merotely can contribute to lessening the stochastic noise in the time for completion of the mitotic process in eukaryotic cells.     

Comparing Stochastic Differential Equations and Agent-Based Modelling and Simulation for Early-Stage Cancer

There is great potential to be explored regarding the use of agent-based modelling and simulation as an alternative paradigm to investigate early-stage cancer interactions with the immune system. It does not suffer from some limitations of ordinary differential equation models, such as the lack of stochasticity, representation of individual behaviours rather than aggregates and individual memory. In this paper we investigate the potential contribution of agent-based modelling and simulation when contrasted with stochastic versions of ODE models using early-stage cancer examples. We seek answers to the following questions: (1) Does this new stochastic formulation produce similar results to the agent-based version? (2) Can these methods be used interchangeably? (3) Do agent-based models outcomes reveal any benefit when compared to the Gillespie results? To answer these research questions we investigate three well-established mathematical models describing interactions between tumour cells and immune elements. These case studies were re-conceptualised under an agent-based perspective and also converted to the Gillespie algorithm formulation. Our interest in this work, therefore, is to establish a methodological discussion regarding the usability of different simulation approaches, rather than provide further biological insights into the investigated case studies. Our results show that it is possible to obtain equivalent models that implement the same mechanisms; however, the incapacity of the Gillespie algorithm to retain individual memory of past events affects the similarity of some results. Furthermore, the emergent behaviour of ABMS produces extra patters of behaviour in the system, which was not obtained by the Gillespie algorithm.     

Modelling the Long-Term Stabilization of Carbon from Maize in a Silty Soil

Soil organic carbon (SOC) models have been widely used to predict SOC change with changing environmental and management conditions, but the accuracy of the prediction is often open to question. Objectives were (i) to quantify the amounts of C derived from maize in soil particle size fractions and at various depths in a long-term field experiment using ¹³C/¹²C analysis, (ii) to model changes in the organic C, and (iii) to compare measured and modelled pools of C. Maize was cultivated for 24 years on a silty Luvisol which resulted in a stock of 1.9 kg maize-derived C m⁻² (36% of the total organic C) in the Ap horizon. The storage of maize-derived C in particle size fractions of the Ap horizon decreased in the order clay (0.65 kg C m⁻²) > fine and medium silt (0.43) > coarse silt (0.33) > fine sand (0.13) > medium sand (0.12) > coarse sand (0.06) and the turnover times of C₃-derived C ranged from 26 (fine sand) to 77 years (clay). The turnover times increased with increasing soil depth. We used the Rothamsted Carbon Model to model the C dynamics and tested two model approaches: model A did not have any adjustable parameters, but included the Falloon equation for the estimation of the amount of inert organic matter (IOM) and independent estimations of C inputs into the soil. The model predicted well the changes in C₃-derived C with time but overestimated the changes in maize-derived C 1.6-fold. In model B, the amounts of IOM and C inputs were optimized to match the measured C₃- and C₄-derived SOC stocks after 24 years of continuous maize. This model described the experimental data well, but the modelled annual maize C inputs (0.41 kg C m⁻² a⁻¹) were less than the independently estimated total input of maize litter C (0.63 kg C m⁻² a⁻¹) and even less than the annual straw C incorporated into the soil (0.46 kg C m⁻² a⁻¹). These results indicated that the prediction of the Rothamsted Carbon Model with independent parameterization served only as an approximation for this site. The total amount of organic C associated with the fraction 0–63 μm agreed well with the sum of the pools ‘microbial biomass’, ‘humified-organic matter’ and IOM of the model B. However, the amount of maize-derived C in this fraction (3.4 g kg⁻¹) agreed only satisfactorily with the sum of maize-derived C in the pools ‘microbial biomass’ and ‘humified organic matter’ (2.6 g kg⁻¹).     

Modelling and Measuring Transpiration from Scots Pine with Increased Temperature and Carbon Dioxide Enrichment

Starting in 1996, individual trees of Scots pine (Pinus sylvestrisL.) aged 30 years, were grown in closed-top chambers and exposedto either normal ambient conditions (CON), elevated CO₂(approx.700 µmol mol^-1; Elev. C), elevated temperature (approx.2 °C and approx. 6 °C above the outside ambient temperatureduring the ‘growing season’ and ‘off season’,respectively; Elev. T) or a combination of elevated CO₂and warmertemperature (Elev. CT). Sap flow was monitored simultaneouslyby the constant-power heat balance method in a total of 16 trees,four for each treatment, over a 32 d period in summer 1998 (afterthe completion of needle expansion and branch elongation). Toquantify the contributions of crown and physical environmentalvariables to total crown transpiration, a ‘sun/shade model’was developed and used to partition the changes in transpirationto different sources. The results of the sap flow measurementsindicate that (1) total daily sap flow (E_tree.d) varied from0.15–3.41 kg per tree; (2) the treatment effect on E_tree.ddependedgreatly on the weather conditions; (3) the cumulative E_tree.dforthe 32 d dropped significantly by 22% relative to CON (P =0.038)under Elev. C and increased significantly by 21% (P =0.043)and 16% (P =0.048) under Elev. T and Elev. CT, respectively.In general, the modelled transpiration gave good agreement withthe sap flow results. The model computations showed that, ona typical sunny day in summer, the effect of treatment on crownstomatal conductance was responsible for approx. 80% of thechange inE_tree.d , while the increase in needle area and theeffect on total radiation absorption contributed only a smallpercentage. Furthermore, sunlit needles were responsible forover 60% of change in transpiration. The effect of the treatmentson E_tree.dwas larger at high temperature and vapour pressuredeficit but was not sensitive to incident daily radiation. Copyright2000 Annals of Botany Company Transpiration model, sap flow, CO₂and temperature elevation, environment-controlled chamber, Pinus sylvestris L.     

Soil Carbon and Nitrogen Fractions and Crop Yields Affected by Residue Placement and Crop Types

Soil labile C and N fractions can change rapidly in response to management practices compared to non-labile fractions. High variability in soil properties in the field, however, results in nonresponse to management practices on these parameters. We evaluated the effects of residue placement (surface application [or simulated no-tillage] and incorporation into the soil [or simulated conventional tillage]) and crop types (spring wheat [Triticum aestivum L.], pea [Pisum sativum L.], and fallow) on crop yields and soil C and N fractions at the 0–20 cm depth within a crop growing season in the greenhouse and the field. Soil C and N fractions were soil organic C (SOC), total N (STN), particulate organic C and N (POC and PON), microbial biomass C and N (MBC and MBN), potential C and N mineralization (PCM and PNM), NH₄-N, and NO₃-N concentrations. Yields of both wheat and pea varied with residue placement in the greenhouse as well as in the field. In the greenhouse, SOC, PCM, STN, MBN, and NH₄-N concentrations were greater in surface placement than incorporation of residue and greater under wheat than pea or fallow. In the field, MBN and NH₄-N concentrations were greater in no-tillage than conventional tillage, but the trend reversed for NO₃-N. The PNM was greater under pea or fallow than wheat in the greenhouse and the field. Average SOC, POC, MBC, PON, PNM, MBN, and NO₃-N concentrations across treatments were higher, but STN, PCM and NH₄-N concentrations were lower in the greenhouse than the field. The coefficient of variation for soil parameters ranged from 2.6 to 15.9% in the greenhouse and 8.0 to 36.7% in the field. Although crop yields varied, most soil C and N fractions were greater in surface placement than incorporation of residue and greater under wheat than pea or fallow in the greenhouse than the field within a crop growing season. Short-term management effect on soil C and N fractions were readily obtained with reduced variability under controlled soil and environmental conditions in the greenhouse compared to the field. Changes occurred more in soil labile than non-labile C and N fractions in the greenhouse than the field.     

Control of Carbon and Electron Flow in Clostridium acetobutylicum Fermentations: Utilization of Carbon Monoxide to Inhibit Hydrogen Production and to Enhance Butanol Yields

Extracts prepared from non-solvent-producing cells of Clostridium acetobutylicum contained methyl viologen-linked hydrogenase activity (20 U/mg of protein at 37°C) but did not display carbon monoxide dehydrogenase activity. CO addition readily inhibited the hydrogenase activity of cell extracts or of viable metabolizing cells. Increasing the partial pressure of CO (2 to 10%) in unshaken anaerobic culture tube headspaces significantly inhibited (90% inhibition at 10% CO) both growth and hydrogen production by C. acetobutylicum. Growth was not sensitive to low partial pressures of CO (i.e., up to 15%) in pH-controlled fermentors (pH 4.5) that were continuously gassed and mixed. CO addition dramatically altered the glucose fermentation balance of C. acetobutylicum by diverting carbon and electrons away from H₂, CO₂, acetate, and butyrate production and towards production of ethanol and butanol. The butanol concentration was increased from 65 to 106 mM and the butanol productivity (i.e., the ratio of butanol produced/total acids and solvents produced) was increased by 31% when glucose fermentations maintained at pH 4.5 were continuously gassed with 85% N₂-15% CO versus N₂ alone. The results are discussed in terms of metabolic regulation of C. acetobutylicum saccharide fermentations to achieve maximal butanol or solvent yield.     

Investigating Factors Affecting Unit-to-Unit Variability in Non-Systemic Pesticide Residues by Stochastic Simulation Modelling

The estimation of acute dietary intake plays a key role in the safety assessment of pesticide residues and needs knowledge of the unit-to-unit variability in residues. There is limited knowledge of contributions of factors to often observed large unit-to-unit variability in residues. A stochastic simulation study was conducted to investigate the effects of sample size and heterogeneity in factors driving residue dissipation of non-systemic pesticides on the unit-to-unit variability among individual apples. The heterogeneity in driving factors was expressed in terms of variability in three dissipation parameters. The variability factor (VF), calculated as the ratio of residues in individual fruit at the 97.5th percentile and the mean residue, was used to represent the unit-to-unit variability. As the rate of dissipation increased, the variability in the corresponding parameter led to larger increases in the variability VF of residues over time. Thus, under field conditions, the relative in pesticide residues is expected to increase with time although the absolute level of residues decreases. The coefficient of variation (CV) was used to describe residue variability in samples of small sizes (5, 10, 20, 40, and 80). When sample size was fewer than 40 fruit, the sample CV increased steeply with decreasing sample size. Measuring residues as concentrations, instead of per fruit, also led to an average 4–8% increase in the CV of residues because of variability in fruit expansion.     

Review of "Stochastic Modelling for Systems Biology" by Darren Wilkinson

"Stochastic Modelling for Systems Biology" by Darren Wilkinson introduces the peculiarities of stochastic modelling in biology. This book is particularly suited to as a textbook or for self-study, and for readers with a theoretical background.     

Mathematical Modelling of Lipase Catalysed Resolution of O-Acetyl and O-Formyl Derivatives of Secondary Alcohols

Lipase catalysed transesterification of O-acetyl and O-formyl derivatives of several sterically hindered secondary alcohols with n-butanol is studied. The reaction is mathematically modelled and the rate constants in the model are evaluated by transient parameter estimation procedure. Several models are considered for predicting the enantiomeric excess (ee) of the product and compared with experimental observations. It is found that the maximum ee depends only on the rate constants of the two competing reactions and not on the order of reaction. A second order model is found to predict the observed behaviour well. When the data is fitted to an equilibrium type of model developed by Chen et al. (1987), it is found that the rate of forward reaction is several orders of magnitude larger than the rate of reverse reaction. The effect of acetyl and formyl groups on the reactivity and selectivity are also discussed.     

Review of "Stochastic Modelling for Systems Biology" by Darren Wilkinson

"Stochastic Modelling for Systems Biology" by Darren Wilkinson introduces the peculiarities of stochastic modelling in biology. This book is particularly suited to as a textbook or for self-study, and for readers with a theoretical background.     

Kinetics and Yields of Pesticide Biodegradation at Low Substrate Concentrations and under Conditions Restricting Assimilable Organic Carbon

The fundamentals of growth-linked biodegradation occurring at low substrate concentrations are poorly understood. Substrate utilization kinetics and microbial growth yields are two critically important process parameters that can be influenced by low substrate concentrations. Standard biodegradation tests aimed at measuring these parameters generally ignore the ubiquitous occurrence of assimilable organic carbon (AOC) in experimental systems which can be present at concentrations exceeding the concentration of the target substrate. The occurrence of AOC effectively makes biodegradation assays conducted at low substrate concentrations mixed-substrate assays, which can have profound effects on observed substrate utilization kinetics and microbial growth yields. In this work, we introduce a novel methodology for investigating biodegradation at low concentrations by restricting AOC in our experiments. We modified an existing method designed to measure trace concentrations of AOC in water samples and applied it to systems in which pure bacterial strains were growing on pesticide substrates between 0.01 and 50 mg liter⁻¹. We simultaneously measured substrate concentrations by means of high-performance liquid chromatography with UV detection (HPLC-UV) or mass spectrometry (MS) and cell densities by means of flow cytometry. Our data demonstrate that substrate utilization kinetic parameters estimated from high-concentration experiments can be used to predict substrate utilization at low concentrations under AOC-restricted conditions. Further, restricting AOC in our experiments enabled accurate and direct measurement of microbial growth yields at environmentally relevant concentrations for the first time. These are critical measurements for evaluating the degradation potential of natural or engineered remediation systems. Our work provides novel insights into the kinetics of biodegradation processes and growth yields at low substrate concentrations.     

Synthetic Chloride-Selective Carbon Nanotubes Examined by Using Molecular and Stochastic Dynamics

Synthetic channels, such as nanotubes, offer the possibility of ion-selective nanoscale pores which can broadly mimic the functions of various biological ion channels, and may one day be used as antimicrobial agents, or for treatment of cystic fibrosis. We have designed a carbon nanotube that is selectively permeable to anions. The virtual nanotubes are constructed from a hexagonal array of carbon atoms (graphene) rolled up to form a tubular structure, with an effective radius of 4.53 Å and length of 34 Å. The pore ends are terminated with polar carbonyl groups. The nanotube thus formed is embedded in a lipid bilayer and a reservoir containing ionic solutions is added at each end of the pore. The conductance properties of these synthetic channels are then examined with molecular and stochastic dynamics simulations. Profiles of the potential of mean force at 0 mM reveal that a cation moving across the pore encounters an insurmountable free energy barrier of ∼25 kT in height. In contrast, for anions, there are two energy wells of ∼12 kT near each end of the tube, separated by a central free energy barrier of 4 kT. The conductance of the pore, with symmetrical 500 mM solutions in the reservoirs, is 72 pS at 100 mV. The current saturates with an increasing ionic concentration, obeying a Michaelis-Menten relationship. The pore is normally occupied by two ions, and the rate-limiting step in conduction is the time taken for the resident ion near the exit gate to move out of the energy well.     

Structural Degradation in Mediterranean Sea Food Webs: Testing Ecological Hypotheses Using Stochastic and Mass-Balance Modelling

Human-mediated disturbances such as fishing, habitat modification, and pollution have resulted in significant shifts in species composition and abundance in marine ecosystems which translate into degradation of food-web structure. Here, we used a comparative ecological modelling approach and data from two food webs (North-Central Adriatic and South Catalan Sea) and two time periods (mid-late 1970s and 1990s) in the Mediterranean Sea to evaluate how changes in species composition and biomass have affected food-web properties and the extent of ecosystem degradation. We assembled species lists and ecological information for both regions and time periods into stochastic structural and mass-balance food-web models, and compared the outcomes of 22 food-web properties. Our results show strong similarities in structural food-web properties between the North-Central Adriatic and South Catalan Seas indicating similar ecosystem structure and levels of ecological degradation between regions and time periods. In contrast, a comparison with other published marine food webs (Caribbean, Benguela, and US continental shelf) suggested that Mediterranean webs are in an advanced state of ecological degradation. This was reflected by lower trophic height, linkage density, connectance, omnivory, species involved in looping, trophic chain length and fraction of biomass at higher trophic levels, as well as higher generality and fraction of biomass at lower trophic levels. An analysis of robustness to simulated species extinction revealed lower robustness to species removals in Mediterranean webs and corroborated their advanced state of degradation. Importantly, the two modelling approaches used delivered comparable results suggesting that they both capture fundamental information about how food webs are structured. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Characterization of Bioluminescent Derivatives of Assimilable Organic Carbon Test Bacteria

The assimilable organic carbon (AOC) test is a standardized measure of the bacterial growth potential of treated water. We describe the design and initial development of an AOC assay that uses bioluminescent derivatives of AOC test bacteria. Our assay is based on the observation that bioluminescence peaks at full cell yield just prior to the onset of the stationary phase during growth in a water sample. Pseudomonas fluorescens P-17 and Spirillum sp. strain NOX bacteria were mutagenized with luxCDABE operon fusion and inducible transposons and were selected on minimal medium. Independent mutants were screened for high luminescence activity and predicted AOC assay sensitivity. All mutants tested were able to grow in tap water under AOC assay conditions. Strains P-17 I5 (with p-aminosalicylate inducer) and NOX I3 were chosen for use in the bioluminescence AOC test. Peak bioluminescence and plate count AOC were linearly related for both test bacteria, though data suggest that the P-17 bioluminescence assay requires more consistent luminescence monitoring. Bioluminescence results were obtained 2 or 3 days postinoculation, compared with 5 days for the ATP luminescence AOC assay and 8 days for the plate count assay. Plate count AOC assay results for nonmutant and bioluminescent bacteria from 36 water samples showed insignificant differences, indicating that the luminescent bacteria retained a full range of AOC measurement capability. This bioluminescence method is amenable to automation with a microplate format with programmable reagent injection.     

Modelling of the baroreflex-feedback mechanism with time-delay

 The cardiovascular system is considered. A direct modelling of the non-linear baroreflex-feedback mechanism, including time-delay, is developed based on physiological theory and empirical facts. The feedback model is then evaluated on an expanded, but simple, non-pulsatile Windkessel model of the cardiovascular system. The stability of the entire model is analyzed and the effect of the value of the time-delay is investigated and discussed. The time-delay may cause oscillations. A finite number of stability switches may occur dependent on the value of the time-delay. The location of these stability switches turns out to be sensitive to the value of the parameters in the model. We suggest a simple experiment to determine whether or not the time-delay is responsible for the 10 second Mayer waves. Data from an ergometer bicycle test is used for evaluation of the model. Received 1 June 1996; received in revised form 20 November 1996     

Valuation of Nature in Conservation and Restoration

Valuation of nature is an important aspect of nature conservation and restoration. Understanding valuation in a broad sense may contribute to conservation strategies since it may lead to better support from society. In this article we propose a model of valuation with respect to conservation and restoration of nature. According to the model, valuation of nature can be characterized by a “valuation approach,” consisting of ecological, ethical and aesthetic perspectives. Such an approach includes scientific and normative aspects and leads to a particular claim of conservation. In this paper we discuss different perspectives, and accordingly, we sketch three main types of these valuation approaches. Political and policy issues with respect to nature conservation and restoration are considered in terms of this model.